Zero-Field Parafermions and Hall Crystals in Moiré Minibands

After the recent experimental realizations of fractional Chern insulators (FCIs) in moiré materials at zero magnetic field, it has been theoretically predicted that non-Abelian states with Majorana fermion excitations may be realized in the nearly dispersionless minibands of these systems. Here, we provide clear evidence based on many-body exact diagonalization for the even more exotic possibility of moiré-based non-Abelian FCIs exhibiting Fibonacci parafermion excitations, which are superior candidates for topological quantum computing. In addition, we predict the emergence of a zero-field Hall crystal with Hall resistance h/e² arising from a partially filled (ν=2/3) moiré band with Chern number C=2 in twisted double bilayer graphene. Our results hint towards the robustness of moiré-based parafermions and of Hall crystals arising from bands with higher Chern number.